If you assume the fleet that Italy actually built is the maximum power they could build, then any improvements or changes would have to come at the price of restrictions elsewhere. If it were up to me, the Italian Navy would let some of the BB conversion/construction go in favor of air wings plus more destroyers and light cruisers... but that's just me.
For my part, I'd rather have a more technically-advanced but smaller force backed up by capable naval air, and I'd want a better submarine doctrine and some kind of decent night-fighting doctrine for the surface fleet. Land-based naval air in theory is an ideal force-multiplier for the Italian Navy but in practice would have two negative qualities. The islands may be unsinkable aircraft carriers, but it is harder to move squadrons from island to island than to move a carrier (in real life - not in the game). And second, the Navy would have to constantly fight off attempts by the Army and Air Force to divert the naval air assets to other purposes. But a strong naval air arm based on Sicily and Malta would go a long way to giving Italy control of the Mediterranean. The British dilemma of having too many demands and not enough ships to meet them all comes into play here; they might let Malta go and try to hang onto Gibraltar and Suez, abandoning the central Med for the near future.
Most of the strategic ideas posted here seem very good to me: use naval and air power to take Malta, then use command of the sea to adequately supply a full-scale assault on Suez (assuming the Army is competent enough to do that). Taking Gibraltar is a great idea in the game but a bad one in the real world for many reasons (most of which were outlined in a thread on the topic) but mostly it boils down to 1) too tough, 2) too important to Spain and 3) unnecessary because your fleet won't go west of the Balearics anyway.
Once Malta is taken and Suez secured, the Italian Navy's role becomes mostly if not purely defensive. Operating in the Atlantic or Indian Ocean takes you out of your air cover and gives the British the chance to chop off whatever you send out. Of course, you could 'mop up' Crete and maybe Cyprus, but if you have control of the Med then those become of secondary importance.